Recently, a new type of .beta.-lactam antibiotic having a sulfo group in 1-position has been found to be recoverable from nature sources and reported [Nature 289, 590 (1981), 291, 489 (1981)]. Syntheses of compounds analogous thereto have also been reported (e.g. Japanese Published unexamined patent application Nos. 164672/1970 and No. 125362/1971). In the latter report is a description of a method for synthesis of 2-azetidinone-1-sulfonic acid compound having a substituent group in 4-position. This method involves a long and complicated series of reaction steps and there has not been developed an expedient synthetic process.